Exact relation between Einstein and quadratic quantum gravity

We show the exact equality of the path integral of the general renormalizable fourth order gravitational action to the path integral of the Einstein action coupled to a massive spin-0 field and a massive spin-2 ghost-like field with non-polynomial interactions. The metric in the Einstein version is a highly nonlinear function of the metric in the quadratic version. Both massive excitations are unstable. The respective cosmological constant terms in the two versions can be very different. Some implications are briefly discussed.